Markov Chains – Springer Series in Operations Research and Financial Engineering – Springer Verlag

This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments.The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods.The book is self-contained, while all the results are carefully and concisely proven.Bibliographical notes are added at the end of each chapter to provide an overview of the literature.Part I lays the foundations of the theory of Markov chain on general states-space.Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques.These two parts can serve as a text on general state-space applied Markov chain theory.Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeperthan that needed to study c